Additive properties of light waves

Thought I’d put this out there as I can’t quite figure it out. So when you have two periodic waves of different frequencies and you add them, you get some sort of resulting wave, which can be simple or complex based upon the difference of frequencies and/or phases. And when you play these back as audio, you can hear each tone in the mixture, plus if they’re close enough, some difference tones or beating. Good so far.

So what I’m wondering is how light waves behave in relation to this. The visible spectrum is approx. 400 to 700 nanometers, give or take, so that’s less than one "octave" of range in frequencies. I’m imagining creating a certain specific frequency, say 700 for a deep red, and mixing that with another, say 530 for a bright green like those cool lasers (great if you shine them off crinkly mylar by the way, hehe). For simplicity’s sake, assume these sources are ideal, that is, like a laser where all wavelengths are the same and in phase.

Anyway, do these wavelengths "mix" or "add" in the same way as the sound wavelengths? I know they will generate another color, but would it essentially be another pure wave, or would it have the characteristically "bumpy" look that you get when mixing two frequencies? What about very close ones that create low-frequency beating, even if the main frequencies are very high? And if they do in fact have this "bumpy" look, then the next question is, Can one create arbitrarily complex periodic waves and turn them into light, or do some kind of simulation of this in Max?

It seems like there’s so many timbres possible with mixing different frequencies of sound, I’m wondering where there are parallels with light and where the parallels break down.

Here’s a simple waveform pic with 2 cycles on the left, 3 on the right, and the middle is the sum (scaled down to fit). If this were scaled to similar-ratio light-wave frequencies and again added, what would the resulting color be?

Just an additional thought about that :
Adding two pure frequencies may generate a color which does not exist in the visible spectrum :
blue + red (quite extrema of the spectrum) gives magenta, which isn’t present in the spectrum : it is a creation of our eyes/brain.

interesting questions. here is another one to add to the mix – light and sound are both described as waves, so it is possible for sound to have its frequency made so high it turns into light? how could this conversion even possibly take place?

It allows you to create and control three "layers" of Left/Right/Combined sine functions (combined by addition, multiplication, or averaging). You choose the coefficients, exponents, offsets, scaling, coloration, playback rate and volume, plus there are some other goodies like automation, sound recording, signal visualization, and a background image/video selector (totally gratuitous but fun). I intended the app to be more of an exploratory learning tool for periodic waves rather than a musical instrument, though there are some nice sounds in there if you get the numbers just right.

I’m also really digging the transparency possibilities in Max 5, which are put to use here in the three levels (three bpatchers on top of each other which swap to the top for user interaction) — you can see everything that’s going on all at once, it’s great!

Sound waves are variations in pressure, while light waves are electromagnetic. So, no sound cannot turn into light just by being at a high frequency. Some sort of transducer is required.

However, sound waves and light waves do have enough in common that a course in optics is often required as part of an acoustics major.

Its been a while since I’ve had a physics class but luckily my googling skills are still up to par. Here is a link to a friendly 2D professor explaining the adding of light waves. Scroll down for a handy interactive visual.

It seems like there’s so many timbres possible with mixing different frequencies of sound, I’m wondering where there are parallels with light and where the parallels break down.

What a thought provoking question! If we mix red and blue we get purple, and we are mixing two different wavelengths to perceive a single color. If we mix two noticeably different wavelengths of sound we’ll hear harmony from two distinct pitches instead of a single pitch. I think we can conclude from this that our sight and hearing operate in very different ways, but beyond that, I’m not sure we understand enough about the brain to resolve this discrepancy.

Perhaps the eyes are ears physically transmit all the different frequency information to our brain, but our perceptual system interprets them in vastly different ways because that’s how we have evolved in order to survive in our environment. We rely on sight so much for basic interaction, perhaps our brain simplifies the frequency information so we can handle it. On the other hand, sound is used for very nuanced communication so maybe we’ve developed a more discerning hearing system?

mixing two different wavelengths in sound is often heard as a single unit. examples of this can be found in virtually every sound outside of a sine wave.

Quite right. I guess I was thinking about the converse, that sound can be perceived as separate pitches. But if you mix red and blue, you’ll see purple instead of some combination of the two distinct colors red+blue.

I don’t think there’s a visual analogy to this? Actually, on cathode ray tube tvs/monitors (or maybe it was due to the lower resolution), you could look real close and see the red/blue/green dots, but as long as you are a normal viewing distance it would merge into a single color. Hmmm…

I would think that if you had two light waves mixed together, and their intensities varied over time, you would perceive something like the purple becoming less red or more blue. But…. yes obviously there are differences in perception between light and sound!

Adding two pure frequencies may generate a color which does not exist in the visible spectrum :
blue + red (quite extrema of the spectrum) gives magenta, which isn’t present in the spectrum : it is a creation of our eyes/brain.

Magenta does exist, but we can’t see chords, and interpret two frequencies as a single color. It is as if our ears could not differentiate between a filtered noise and a sine wave. We have only a three band filter for determining color, and the span for light is only about one octave…